Casimir Rack and Pinion

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					Casimir Rack and Pinion
           Ramin Golestanian
    Department of Physics and Astronomy
          University of Sheffield
    Significance of Casimir Force

• Tiny at Micron-scale
        It took 50 years to be verified!

• Dominant at Nano-scale
        Strongest distance dependence


      unwanted effects: stiction

      harnessed for good use: novel NEMS
          Geometry Challenge

• Practical Aspect
  Realistic ``machine parts’’


• Fundamental Aspect
  Pair-wise summation?
                  Geometry Challenge

• Expansion in Dielectric Contrast




                                                      Not so easy …
 R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)
                  Geometry Challenge

• Convergence properties




 CM:



 R. Golestanian, Phys. Rev. Lett. 95, 230601 (2005)
         Normal Casimir Force

• Is it practical in making nano-mechanical
  devices?
  Not really …



• Repulsive Casimir Force: does it exist?



                       Alchemy of nano-mechanics …
               Lateral Casimir Force

• Theoretical Prediction
   ``Josephson-like’’ force
     between corrugated
     surfaces




R. Golestanian & M. Kardar, Phys. Rev. Lett. 78, 3421 (1997)
T. Emig, A. Hanke, R. Golestanian & M. Kardar, Phys. Rev. A 67, 022114 (2003)
              Lateral Casimir Force

• Experimental Verification




 F. Chen, U. Mohideen, G. L. Klimchitskaya, &
 V. M. Mostepanenko, Phys. Rev. Lett. 88, 101801 (2002)
                       Rack and Pinion

 Powered by Quantum
  Vacuum

 Force transduction
  with no contact could
  potentially solve
  wear problem in
  nano-mechanical
  systems



  A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. Lett. 98, 140801 (2007)
           Equation of Motion
           y


           H                      l
x=Rq

           q                  y
               R          x




       W
             Equation of Motion

 Relevant parameters:




 Uniformly moving rack:
                 No Dissipation

 The equation is integrable: nonlinear pendulum




 Skipping Velocity:
                  No Dissipation

 Pinion Velocity vs Rack Velocity and initial Offset
                  No Dissipation

 The effect of external load on the skipping transition




                                similar to solid friction
               Weak Dissipation

 The skipping transition boundary
               Weak Dissipation

 Pinion Velocity vs Rack Velocity and Load
                Strong Dissipation

 Pinion Velocity vs Rack Velocity and Load




 Stall Force
            Vibrating Rack and Pinion

 Is it possible to rectify a symmetric oscillatory
  motion?




  A. Ashourvan, M.F. Miri, & R. Golestanian, Phys. Rev. E 75, 040103 (R)(2007)
   See also: T. Emig, Phys. Rev. Lett. 98, 160801 (2007)
         Vibrating Rack and Pinion

 Equation of motion:




 Solution:




 Pinion Velocity:
         Vibrating Rack and Pinion

 Basin of attraction for forward motion
         Vibrating Rack and Pinion

 Parameter values for forward motion




 Stall Force:
                     Feasibility

 Realistic values for the lateral Casimir force amplitude
                      Feasibility

 Realistic values for skipping velocity




                                           Not so small after all …
                    Conclusion
 Casimir forces are dominant at nano-scale ☺
 Knowledge of Casimir forces can be used to avoid
  unwanted effects in NEMS
 They can be used to design nano-mechanical devices:
  mechanical engineering with quantum vacuum fluctuation
  forces!
 Non-contact lateral force transduction can solve the
  wear problem
 Despite expectation, the Casimir grip can be strong
Collaborators:
A. Ashourvan (IASBS, Zanjan)
M.F. Miri (IASBS, Zanjan)


Acknowledgement:




                               THANK YOU

				
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posted:5/24/2012
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